PSI - Issue 42

Alla V. Balueva et al. / Procedia Structural Integrity 42 (2022) 9–17 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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the present, only few atomistic level calculations of the reactions of the various coatings on some substrates are available in the literature [Balueva et al., 2017, 2019, 2020; Grubova et. al., 2017, 2019; Jami and Jabbarzadeh, 2019a, 2019b, 2020]. Recent publications in dentistry reveal that it is not advisable to merely apply the tricalcium phosphate/HAp to the titanium directly; it is better for the titanium to oxidize then apply the tricalcium phosphate on the layer of titanium dioxide formed on top of the substrate [Tsygankov, P.A., et al. (2019)]. In this paper we make numerical calculations of adhesion strength of Tricalcium phosphate on titanium dioxide, by first principals of physical chemistry. There are not many calculations on calcium phosphate coatings in the current literature. It is the topic of this paper to suggest a model of molecular calculation of the adhesive strength of the tricalcium phosphate coating on the titanium dioxide dental implant substrate. This is done by calculating the binding energy between titanium dioxide and tricalcium p hosphate. We slowly “build up” tricalcium phosphate by binding its constituent parts with titanium dioxide until we reach the chemical formula for a full cell of tricalcium phosphate. Using Density Functional Theory, we modelled a reaction and then calculated the bonding energy of titanium dioxide TiO 2 with the constituents of a tricalcium phosphate coating, Ca 3 (PO 4 ) 2 , which then used to calculate the adhesion strength of tricalcium phosphate and compare it with the known experimental data. 2. Method of calculation of adhesion strength of Tricalcium Phosphate Ca 3 (PO 4 ) 2 on Ti Density Functional Theory is a theory of approximations on the quantum level that allows a novel method of solving Schrodinger’s equation. Instead of relying on solving it for the wavefunction directly, it is possible to solve it by minimization of a quadratic functional for the electron density [Laird et. al., 1996; Koch et. al., 2001]. Then conducting minimization of the functional for many particles using the DFT functional RB3YLP in Gaussian 09 software, these geometry optimizations give the necessary positions of nuclei that deliver a global minimum on the potential energy surface. The time-independent Schrodinger equation, which describes the interactions of N particles: ̂ ( 1 , 2 , . . . ) = ( 1 , 2 , . . . ), (2.1) where Ĥ is Hamiltonian, is a wave function, E is the total energy for the system. In Density Functional Theory it is assumed that the kinetic energy of electrons is much greater than the kinetic energy of nuclei, meaning the nuclei are believed to be fixed (at ground state). We can then see that the Schrodinger equation now becomes ̂ ( ⃑, ⃑⃑ ) = ( ⃑ ) ( ⃑, ⃑⃑ ). (2.2) where ̂ is the electronic Hamiltonian, and eigenvalues will give the ground-state energy of the nuclei. According to Density Functional Theory, the reactants and products are both at the positions of the absolute minima on the potential energy surface [Carr et. al., 2005]. From energy principals, the path between reactants and products goes in the direction of minimum spending energy, which is the path through a saddle point between two global minima on the potential energy surface. The difference between the saddle point energy and the reactant energy will give the activation energy barrier, E act , or the energy that is needed to be overcome to form a bond. The difference in reactants energy and the product energy will give the binding energy or the energy stored in the product compared with the reactants. Multiplying Eg. (2.2) by ⃐⃑